This article on inversion, from Perfect English Grammar.com [corrected and modified], explains the construction and the transformation involved:
4: We use inversion after 'so + adjective' where later followed by 'that':
So beautiful was the girl that nobody could talk of anything else. (Normal sentence: the girl was so beautiful that nobody could talk of
So delicious was the food that we ate every last bite. (Normal sentence: the food was so delicious that we ate every last bite.)
The inverted variants are rather old-fashioned or of a literary register. Equally so is the further re-ordering:
So prevalent is the use of cars that we cannot imagine life without
We cannot image life without cars, so prevalent is their use.
The terminal positioning of the clause giving the reason is acceptable; here is an example from Belloc (The Path to Rome - Page 245):
Above the soft bed which the hay made, a square window, unglazed, gave
upon the southern night; the mist hardly drifted in or past it, so
still was the air.